How can I create a flowing, rippling water surface effect that follows the curves of a river mesh?
One of the tricky things about rivers is how to animate the water ripples along the path of the curving river. The best way that I have found to do this is by adding a Displacement Modifier set to UV texture coordinates and using a Noise/Cloud texture as well as UV unwrapping the mesh first before extrusion.



There are two important secrets to this technique. 


One is UV unwrapping the river water mesh as a straight line first before you alter it to fit the river shape. If you start with a plane, unwrap it right away, then the UV map will stay straight even if you extrude the plane edges to form the curved river shape.







Secondly, you need to enable the AnimAll addon so that you can
animate the UV map. 




Once you do that you can set two keyframes for
    the UV map and then animate it moving from top to bottom. In the Tools panel on the left, choose the Animation tab (after enabling the AnimAll addon). Select the UV checkbox, and click the Insert keyframe button at the appropriate frames after moving the UV map.






This will
    move the texture image along the river and will also move the
    displacement along the river. Once your UV's are set and animated you can use those texture coordinates for material textures or displacement modifier textures.





Here's a test scene using this technique: